In an Order Statistic Tree which is also AVL, if the dimension of the left subtree is 2, what is the maximum dimension of the right subtree? What I think is that we can add 6 nodes in the right subtree, one has two children, and the two children have as well two. And this will not affect the AVL property, so my answer is the dimension of the right subtree is 7, but I am not sure.
The determining factor is that it is an AVL tree. Whether or not it is also an order statistic tree does not influence the maximum number of nodes that can occur in the right subtree.
We're given that the left subtree has 2 nodes, so that means the left child of the root has one child, which is a leaf. This means the left subtree has a height of 1. Because of the AVL property, the right subtree will either have a height of 0, 1 or 2. As we want to maximize the number of nodes in the right subtree, we'll go for a height of 2 and fill it up to be a perfect binary tree:
_o_
/ \
o _o_
/ / \
o o o
/ \ / \
o o o o
And so the right subtree can have at most 7 nodes. Adding one more would violate the AVL property.